Russia said the International Red Cross will help transport injured rebels out of the city.
Those leaving Aleppo would head for Idlib province to the west of the city.
The world is about to learn what happens when the U.S. recuses itself from moral leadership.
A ceasefire agreement was reached after reports of summary executions in the city.
The battle of Aleppo, one of the worst of a civil war that has drawn in global and regional powers, has ended with victory for Syrian President Bashar al-Assad.
The British foreign secretary said the 2013 vote against intervention had limited the U.K.'s ability to influence events in Syria.
On Monday, rebel defences in the city collapsed, leading to a broad army advance.
The Syrian military, backed by Russia, is on the brink of recapturing the northern city.
Moscow said that the Syrian army had halted military activity to let civilians leave rebel-held territory.
The Syrian army have made rapid gains against insurgents in the past two weeks and look closer than ever to restoring full control over Aleppo.
Ruslan Galitsky is the 23rd Russian national to be officially confirmed dead in Syria.
President Assad's forces now control more than two-thirds of the city.
Foreign Minister Jean-Marc Ayrault says the "humanitarian disaster" in Aleppo must end.
Turkey already conducts operations in the U.S. against those with whom Erdogan disagrees.
The loss of territory in Aleppo is the biggest defeat for rebels in the city since 2012.
Civilian volunteers say the lack of medical supplies and aid will leave many facing death.